View source for Elementary interval

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''of a partially ordered set''

A subset consisting of two elements $a\leq b$ such that there are no other elements in the [[partially ordered set]] between them, i.e.

$$a\leq x\leq b\Rightarrow a=x\text{ or }a=b.$$



====Comments====
Elementary intervals are also called gaps or simple or atomic intervals.

For (elementary) intervals in $\mathbf R$ see [[Interval and segment|Interval and segment]]; [[Interval, closed|Interval, closed]]; [[Interval, open|Interval, open]].

One says that in this situation, $b$ is a ''[[covering element]]'' of, or ''covers'' $a$.

[[Category:Order, lattices, ordered algebraic structures]]

{{SourceattributionEOM|Elementary interval}}
[[Category:Mathematics]]